WASHINGTON — Freed from the constraint of a presidential veto, Republicans are moving rapidly on industry-backed legislation that could paralyze the government’s ability to protect the environment, public health and virtually everything else federal agencies regulate.

The onslaught began last week with a trio of House bills — two of them approved and sent to the Senate — that would gut the administrative process used for decades to implement the practical details of such landmark laws as the Food and Drug Act, the Clean Air Act and the Fair Labor Standards Act.

The centerpiece of the Republican action was the REINS Act, which cleared the House on Friday, with an amendment that extended its reach to include all regulations adopted by federal agencies within the past 10 years. Approved on a largely party-line vote, it swiftly drew companion Senate legislation.

The act would require any rule costing industry more than $100 million — a dollar figure that amounts to any significant regulation — to be submitted to Congress. If either chamber fails to approve the rule within 70 days, the rule would die.

The rules could affect everything from food labeling and nutrition requirements for restaurants to performance standards for residential wood stoves and energy efficiency standards in grocery store coolers to banking and public health. One major rule adopted after the financial crisis requires banks to hold larger cash reserves. A 2014 rule cleans up tailpipe emissions from cars. A 2009 rule for the first time allowed regulation of tobacco.

The regulations result from acts of Congress, which approve laws such as the Clean Air Act or the Dodd-Frank financial overhaul bill, but leave the regulations that serve to implement the laws to experts in the federal agencies. As a practical matter, the Republican bills would shift regulatory power from executive branch agencies bound by scientific and legal protocols to the political realm of Congress.